Elongated triangular gyrobicupola

Elongated triangular gyrobicupola
(3D model) (OFF file)
Rank	3
Type	CRF
Notation
Bowers style acronym	Etigybcu
Coxeter diagram	oxxx3xxxo&#xt
Elements
Faces	2+6 triangles 6+6 squares
Edges	6+6+6+6+12
Vertices	6+12
Vertex figures	6 rectangles, edge lengths 1 and √2
	12 isosceles trapezoids, edge lengths 1, √2, √2, √2
Measures (edge length 1)
Volume	${\frac {10{\sqrt {2}}+9{\sqrt {3}}}{6}}\approx 4.95510$
Dihedral angles	3–4 join: $\arccos \left(-{\frac {2{\sqrt {2}}}{3}}\right)\approx 160.52878^{\circ }$
	4–4 join: $\arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$
	3–4 cupolaic: $\arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }$
	4–4 prismatic: 120°
Central density	1
Number of external pieces	20
Level of complexity	12
Related polytopes
Army	Etigybcu
Regiment	Etigybcu
Dual	Gyrodeltodeltoidal octadecahedron
Conjugate	None
Abstract & topological properties
Flag count	144
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	(G2×A1)/2, order 12
Flag orbits	12
Convex	Yes
Nature	Tame

The elongated triangular gyrobicupola (OBSA: etigybcu) is one of the 92 Johnson solids (J₃₆). It consists of 2+6 triangles and 6+6 squares. It can be constructed by inserting a hexagonal prism between the two halves of the cuboctahedron, seen as a triangular gyrobicupola.

Vertex coordinates

An elongated triangular gyrobicupola of edge length 1 has the following vertices:

• $\left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {1}{2}}\right)$,
• $\left(\pm 1,\,0,\,\pm {\frac {1}{2}}\right)$,
• $\pm \left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,{\frac {3+2{\sqrt {6}}}{6}}\right)$,
• $\pm \left(0,\,{\frac {\sqrt {3}}{3}},\,{\frac {3+2{\sqrt {6}}}{6}}\right)$.

External links

• Klitzing, Richard. "etigybcu".
• Quickfur. "The Elongated Triangular Gyrobicupola".

• Wikipedia contributors. "Elongated triangular gyrobicupola".
• McCooey, David. "Elongated Triangular Gyrobicupola"